This is the classical Pearson's \(\chi ^2\)  test statistic for fitting the frequencies of \({\text{\bfseries \ttfamily H}}\)  and \({\text{\bfseries \ttfamily T}}\)  to the distribution \((0.5,0.5)\)  [1]}. This fact extends to any finite-dimensional distribution vector \(\mathbf {p}\) . The combination \(\sum _{{\text{\bfseries \ttfamily x}}}\bar{\#} {\text{\bfseries \ttfamily x}}{\text{\bfseries \ttfamily x}}/p_{{\text{\bfseries \ttfamily x}}} - 1\) , which is essentially Pearson's \(\chi ^2\)  statistic, always lies in \(W_{220}\) .
